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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.16453 |
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| _version_ | 1866917812392427520 |
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| author | Rhodes, Anthony Jiang, Bin Jiang, Jenny |
| author_facet | Rhodes, Anthony Jiang, Bin Jiang, Jenny |
| contents | Non-negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi-Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts-based data representations to include mixed-sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF-related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new $L_{2,1}$ SNF algorithm that utilizes the noise-insensitive $L_{2,1}$ norm. We provide monotonic convergence analysis of the $L_{2,1}$ SNF algorithm. In addition, we conduct numerical experiments on three benchmark mixed-sign datasets as well as several randomized mixed-sign matrices to demonstrate the performance superiority of $L_{2,1}$ SNF over conventional SNF algorithms under the influence of Gaussian noise at different levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph Regularized Sparse $L_{2,1}$ Semi-Nonnegative Matrix Factorization for Data Reduction Rhodes, Anthony Jiang, Bin Jiang, Jenny Numerical Analysis Non-negative Matrix Factorization (NMF) is an effective algorithm for multivariate data analysis, including applications to feature selection, pattern recognition, and computer vision. Its variant, Semi-Nonnegative Matrix Factorization (SNF), extends the ability of NMF to render parts-based data representations to include mixed-sign data. Graph Regularized SNF builds upon this paradigm by adding a graph regularization term to preserve the local geometrical structure of the data space. Despite their successes, SNF-related algorithms to date still suffer from instability caused by the Frobenius norm due to the effects of outliers and noise. In this paper, we present a new $L_{2,1}$ SNF algorithm that utilizes the noise-insensitive $L_{2,1}$ norm. We provide monotonic convergence analysis of the $L_{2,1}$ SNF algorithm. In addition, we conduct numerical experiments on three benchmark mixed-sign datasets as well as several randomized mixed-sign matrices to demonstrate the performance superiority of $L_{2,1}$ SNF over conventional SNF algorithms under the influence of Gaussian noise at different levels. |
| title | Graph Regularized Sparse $L_{2,1}$ Semi-Nonnegative Matrix Factorization for Data Reduction |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.16453 |